Effective Variance

 

A similar analysis was carried out studying the impact of effective variance. Values of effective variance reported in the literature vary widely from 0.02-0.86 (Kent et al., 1995). The effects of varying $v_{\rm eff}$ from 0.07 to 0.57, in increasing increments to account for the fact that the actual log-normal width parameter is proportional to $\ln{(1+v_{\rm {eff}})}$, are examined. Calculations are shown in Figure 5.9 at 750 nm. There is little impact on the radiances. The impact on the polarization seemed to vary widely from a maximum of 0.04 between $v_{\rm eff}=0.07$ to 0.17, the two narrowest distributions, to a minimum of 0.01 between $v_{\rm eff}=0.37$ to 0.57, the two widest distributions. To investigate if other geometries might be better suited and produce a larger variation, the -P₂₁/P₁₁ ratio was examined. From Figure 5.10, it is clear that polarization is not a strong function of effective variance except for narrow distributions. In fact for $v_{\rm eff}>0.25$, polarization remains essentially constant. Also, the behaviour of polarization with scattering angle (and hence elevation angle) is very similar at all values of effective variance except for $v_{\rm eff}<0.07$. For the larger particles, 0.25-0.30 $\mu$m, the glory can again be exploited as the peak of the hill is rapidly washed with wider distributions. It appears that the degree to which effective variance can be retrieved varies considerably for this geometry.

  

Figure 5.10: Fraction of light polarized after single-scattering of unpolarized incident radiation as a function of effective variance, $v_{\rm eff}$, and scattering angle at 750 nm.